taiwan-gsat 2024 Q20

taiwan-gsat · Other · gsat__math-a 8 marks Vectors: Lines & Planes Multi-Step Geometric Modeling Problem
In coordinate space, let $O$ be the origin and $E$ be the plane $x - z = 4$.
Continuing from question 19, it is known that point $P$ is on plane $E$ and $b = 0$. Find the maximum possible range of $c$ and the minimum possible length of line segment $\overline{OP}$. (Non-multiple choice question, 8 points)
In coordinate space, let $O$ be the origin and $E$ be the plane $x - z = 4$.

Continuing from question 19, it is known that point $P$ is on plane $E$ and $b = 0$. Find the maximum possible range of $c$ and the minimum possible length of line segment $\overline{OP}$. (Non-multiple choice question, 8 points)